I'd probably carry the 7x57. Any of the three will work but both .250 Savage and .32 Special are sliding dangerously close to what I'd consider minimum power for whitetail. Still within the acceptable range, but very close to the edge of it.
7x57 on the other hand is in the "optimal" range of the scale rather than merely being "acceptable".
FWIW my go-to cartridge for whitetail is 7mm-08 which is ballistically nearly the same as 7x57. I've hunted with as low of power as .225 Winchester and as high as .30-06 but to me 7mm-08 is "just right".
7x57 on the other hand is in the "optimal" range of the scale rather than merely being "acceptable".
FWIW my go-to cartridge for whitetail is 7mm-08 which is ballistically nearly the same as 7x57. I've hunted with as low of power as .225 Winchester and as high as .30-06 but to me 7mm-08 is "just right".